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difference between elastic limit and proportional limit

hi all,

can anyone explain about the following basic questions

1. me the difference between the proportional limit and elastic limit.

   Please dont give the definitions of both, i need some detailed explaination.

 2. How many natural frequency a object can have?




1. the difference can be understood from the definitions itself:

- proportional limit is strain below which the stress is proportional to strain i.e. linear relation between the two. e.g.  sigma=E*epsilon for steel.

- elastic limit is strain below which the material can regain its original shape if the forces are release, doesn't matter if the stress-strain relation is linear or not. for example rubber. the strain-strain law is highly non-linear (and hence not "proportional") but still elastic.


2. number of natural frequencies (or natural modes of vibration) depend on number of degrees of freedom (DOF). i.e. number of possible different (unique) ways a body can be deformed. in reality, every body has infinite number of particles (nothing is absolutely rigid) and therefore infinite number of DOFs => infinite number of natual frequencies. practically, only frequencies that are in the range of interest (that affect behavior in operating range of freq) are important. these can be obtained from analytical or computational models. for example, in FEM, the no of natural freq is total number of DOF of the model.  the more DOF u include (finer mesh),  the closer it gets to reality.

materails exhibiting behaviour 1 (jj post above) are termed as "hypoelastic"

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